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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 47040.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.n1 | 47040i1 | \([0, -1, 0, -796021, -181486955]\) | \(463030539649024/149501953125\) | \(18010885410000000000\) | \([2]\) | \(1290240\) | \(2.3982\) | \(\Gamma_0(N)\)-optimal |
47040.n2 | 47040i2 | \([0, -1, 0, 2266479, -1242949455]\) | \(667990736021936/732392128125\) | \(-1411730661077452800000\) | \([2]\) | \(2580480\) | \(2.7448\) |
Rank
sage: E.rank()
The elliptic curves in class 47040.n have rank \(0\).
Complex multiplication
The elliptic curves in class 47040.n do not have complex multiplication.Modular form 47040.2.a.n
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.